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Generalised Gaussian radial basis function neural networks

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Abstract

The mixed use of different shapes of radial basis functions (RBFs) in radial basis functions neural networks (RBFNNs) is investigated in this paper. For this purpose, we propose the use of a generalised version of the standard RBFNN, based on the generalised Gaussian distribution. The generalised radial basis function (GRBF) proposed in this paper is able to reproduce other different radial basis functions (RBFs) by changing a real parameter τ. In the proposed methodology, a hybrid evolutionary algorithm (HEA) is employed to estimate the number of hidden neuron, the centres, type and width of each RBF associated with each radial unit. In order to test the performance of the proposed methodology, an experimental study is presented with 20 datasets from the UCI repository. The GRBF neural network (GRBFNN) was compared to RBFNNs with Gaussian, Cauchy and inverse multiquadratic RBFs in the hidden layer and to other classifiers, including different RBFNN design methods, support vector machines (SVMs), a sparse probabilistic classifier (sparse multinominal logistic regression, SMLR) and other non-sparse (but regularised) probabilistic classifiers (regularised multinominal logistic regression, RMLR). The GRBFNN models were found to be better than the alternative RBFNNs for almost all datasets, producing the highest mean accuracy rank.

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Notes

  1. http://www.uco.es/grupos/ayrna/index.php?lang=en (“Datasets” section).

  2. http://www.cns.atr.jp/~oyamashi/SLR-WEB/.

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Acknowledgments

This work has been partially subsidised by the TIN2011-22794 project of the Spanish Inter-Ministerial Commission of Science and Technology (MICYT), FEDER funds and the P08-TIC-3745 project of the “Junta de Andalucia” (Spain).

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Authors and Affiliations

  1. Advanced Concept Team (ACT), European Space Research and Technology Centre (ESTEC), European Space Agency (ESA), Noordwijk, Netherlands

    F. Fernández-Navarro

  2. Department of Computer Science and Numerical Analysis, University of Córdoba, Córdoba, Spain

    C. Hervás-Martínez & P. A. Gutierrez

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  1. F. Fernández-Navarro
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  2. C. Hervás-Martínez
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  3. P. A. Gutierrez
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Correspondence to F. Fernández-Navarro.

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Fernández-Navarro, F., Hervás-Martínez, C. & Gutierrez, P.A. Generalised Gaussian radial basis function neural networks. Soft Comput 17, 519–533 (2013). https://doi.org/10.1007/s00500-012-0923-4

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